assn06

src/assn06/AVLTree.java

@@ -0,0 +1,203 @@
+package assn06;
+
+public class AVLTree<T extends Comparable<T>> implements SelfBalancingBST<T> {
+    // Fields
+    private T _value;
+    private AVLTree<T> _left;
+    private AVLTree<T> _right;
+    private int _height;
+    private int _size;
+
+    public AVLTree() {
+        _value = null;
+        _left = null;
+        _right = null;
+        _height = -1;
+        _size = 0;
+    }
+
+    private void updateMeta() {
+        this._height = 1 + Math.max(this._left.height(), this._right.height());
+        this._size = 1 + this._left.size() + this._right.size();
+    }
+
+    /**
+     * Rotates the tree left and returns
+     * AVLTree root for rotated result.
+     */
+    private AVLTree<T> rotateLeft() {
+        if (isEmpty())
+            throw new RuntimeException("Illegal operation on empty tree");
+
+        AVLTree<T> newRoot = this._right;
+        this._right = newRoot._left;
+        newRoot._left = this;
+
+        newRoot._left.updateMeta();
+        newRoot.updateMeta();
+
+        return newRoot;
+    }
+
+    /**
+     * Rotates the tree right and returns
+     * AVLTree root for rotated result.
+     */
+    private AVLTree<T> rotateRight() {
+        if (isEmpty())
+            throw new RuntimeException("Illegal operation on empty tree");
+
+        AVLTree<T> newRoot = this._left;
+        this._left = newRoot._right;
+        newRoot._right = this;
+
+        newRoot._right.updateMeta();
+        newRoot.updateMeta();
+
+        return newRoot;
+    }
+
+    @Override
+    public boolean isEmpty() {
+        return size() == 0;
+    }
+
+    @Override
+    public int height() {
+        return _height;
+    }
+
+    @Override
+    public int size() {
+        return _size;
+    }
+
+    private int balanceFactor() {
+        return _left.height() - _right.height();
+    }
+
+    private SelfBalancingBST<T> rebalance() {
+        AVLTree<T> self = this;
+        self.updateMeta();
+
+        if (self.balanceFactor() > 1)
+            if (self._left.balanceFactor() < 0) {
+                self._left = self._left.rotateLeft();
+                self = self.rotateRight();
+            } else
+                self = self.rotateRight();
+        else if (self.balanceFactor() < -1)
+            if (self._right.balanceFactor() > 0) {
+                self._right = self._right.rotateRight();
+                self = self.rotateLeft();
+            } else
+                self = self.rotateLeft();
+
+        return self;
+    }
+
+    @Override
+    public SelfBalancingBST<T> insert(T element) {
+        if (isEmpty()) {
+            _value = element;
+            _left = new AVLTree<T>();
+            _right = new AVLTree<T>();
+            _height = 0;
+            _size = 1;
+
+            return this;
+        }
+
+        if (_value.compareTo(element) > 0)
+            _left = (AVLTree<T>) _left.insert(element);
+        else if (_value.compareTo(element) < 0)
+            _right = (AVLTree<T>) _right.insert(element);
+
+        return this.rebalance();
+    }
+
+    @Override
+    public SelfBalancingBST<T> remove(T element) {
+        if (!contains(element))
+            return this;
+
+        if (_value.compareTo(element) > 0)
+            _left = (AVLTree<T>) _left.remove(element);
+        else if (_value.compareTo(element) < 0)
+            _right = (AVLTree<T>) _right.remove(element);
+        else {
+            if (_left.isEmpty() && _right.isEmpty())
+                return new AVLTree<T>();
+            else if (_left.isEmpty())
+                return _right;
+            else if (_right.isEmpty())
+                return _left;
+            else {
+                _value = _right.findMin();
+                _right = (AVLTree<T>) _right.remove(_value);
+            }
+        }
+
+        return this.rebalance();
+    }
+
+    @Override
+    public T findMin() {
+        if (isEmpty()) {
+            throw new RuntimeException("Illegal operation on empty tree");
+        }
+        if (_left.isEmpty()) {
+            return _value;
+        } else {
+            return _left.findMin();
+        }
+    }
+
+    @Override
+    public T findMax() {
+        if (isEmpty()) {
+            throw new RuntimeException("Illegal operation on empty tree");
+        }
+        if (_right.isEmpty()) {
+            return _value;
+        } else {
+            return _right.findMax();
+        }
+    }
+
+    @Override
+    public boolean contains(T element) {
+        if (isEmpty())
+            return false;
+
+        if (_value.compareTo(element) == 0)
+            return true;
+        else if (_value.compareTo(element) > 0)
+            return _left.contains(element);
+        else
+            return _right.contains(element);
+
+    }
+
+    @Override
+    public T getValue() {
+        return _value;
+    }
+
+    @Override
+    public SelfBalancingBST<T> getLeft() {
+        if (isEmpty()) {
+            return null;
+        }
+        return _left;
+    }
+
+    @Override
+    public SelfBalancingBST<T> getRight() {
+        if (isEmpty()) {
+            return null;
+        }
+        return _right;
+    }
+
+}

src/assn06/Main.java

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+package assn06;
+
+public class Main {
+    public static void main(String[] args) {
+
+        // Create a new empty tree.
+        SelfBalancingBST<Integer> avl_bst = new AVLTree<Integer>();
+
+        // Insert 50 random integers.
+        // Note how we need to capture the result of insert back into
+        // the variable avl_bst because the post-insertion root that is
+        // returned may be different from the original root because of the insertion.
+        // result should be about 6.
+
+        for (int i = 0; i < 50; i++) {
+            int rand = (int) (Math.random() * 100);
+            while (avl_bst.contains(rand))
+                rand = (int) (Math.random() * 100);
+
+            avl_bst = avl_bst.insert(rand);
+        }
+        System.out.println("\nheight: " + avl_bst.height());
+        System.out.println("size: " + avl_bst.size());
+
+        // Now insert 50 integers in increasing order which would
+        // cause a simple BST to become very tall but for our
+        // self-balancing tree won't be too bad (should be 7)
+
+        for (int i = 150; i < 200; i++) {
+            avl_bst = avl_bst.insert(i);
+        }
+        System.out.println("\nheight: " + avl_bst.height());
+        System.out.println("size: " + avl_bst.size());
+
+        // test remove
+        avl_bst = avl_bst.remove(avl_bst.findMax());
+        avl_bst = avl_bst.remove(avl_bst.findMin());
+
+        System.out.println("\nheight: " + avl_bst.height());
+        System.out.println("size: " + avl_bst.size());
+    }
+}

src/assn06/SelfBalancingBST.java

@@ -0,0 +1,76 @@
+package assn06;
+
+public interface SelfBalancingBST<T extends Comparable<T>> {
+
+    /**
+     * @return true if the tree is empty
+     */
+    boolean isEmpty();
+
+    /**
+     * @return height of the tree.
+     */
+    int height();
+    
+    /**
+     * @return the number of elements in the tree
+     */
+    int size();
+
+    /**
+     * Inserts element into tree and returns resulting
+     * tree (i.e. root) after insertion. Depending on implementation,
+     * this may or may not be the same object that you started with.
+     * @param element to be added to the tree
+     * @return resulting tree after insertion
+     **/
+    SelfBalancingBST<T> insert(T element);
+
+    /**
+     * Removes element from tree and returns resulting
+     * tree after removal. Depending on implementation,
+     * this may or may not be the same object that you
+     * started with. If element is not in the tree, the
+     * tree should remain unchanged and return itself.
+     * @param element to be removed from the tree
+     * @return resulting tree after removal
+     **/
+    SelfBalancingBST<T> remove(T element);
+
+    /**
+     * Throws a RuntimeException if called on an empty tree.
+     * @return the smallest value in the tree
+     */
+    T findMin();
+
+    /**
+     * Throws a RuntimeException if called on an empty tree.
+     * @return the smallest value in the tree.
+     */
+    T findMax();
+
+    /**
+     * @param element whose presence in this tree is to be tested
+     * @return true if this tree contains the specified element
+     */
+    boolean contains(T element);
+
+    /**
+     * @return value at the top of the tree.
+     * If a tree is empty, its value is null.
+     */
+    T getValue();
+
+    /**
+     * @return the left child of the tree.
+     * Throws a RuntimeException if the tree is empty.
+     */
+    SelfBalancingBST<T> getLeft();
+
+    /**
+     * @return the right child of the tree.
+     * Throws a RuntimeException if the tree is empty.
+     */
+    SelfBalancingBST<T> getRight();
+
+}